Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized- Time Integration

In this paper, the direct differentiation of generalized-alpha time integration is derived, equations are introduced and results are shown. Although generalized-alpha time integration has found usage, the derivation and the resulting equations for the analytical sensitivity analysis via direct differentiation are missing. Thus, here, the sensitivity equations of generalized-alpha time integration via direct differentiation are provided. Results with generalized-alpha are compared with Newmark-beta time integration and their sensitivities with numerical sensitivities via forward finite differencing in terms of accuracy and performance. An example is shown for each linear structural dynamics and flexible multibody dynamics.